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Matt Enlow made a great comment here...

So my advice would just be, what math ideas are you curious about? Find other problem sources, and see if any problems spark your interest and lead you to ask other questions (of yourself): Will that always be the case? Does that trick always work? What if you consider rational numbers, instead of just integers? Etc., etc. The more you get in the habit of asking yourself questions, the more naturally question-asking will come in general.